Stiffened composite structures are structures that are constructed of composite materials, such as fiber reinforced composite materials, and typically include some form of structural support that carries a skin. Some modern aircraft fuselages are examples of stiffened composite structures that include a skin operatively coupled to (i) frame members that extend circumferentially around and that are spaced longitudinally along the inside of the fuselage and (ii) stringers that extend longitudinally along and that are spaced circumferentially around the inside of the fuselage. A common stringer configuration utilized in stiffened composite fuselages are referred to as hat-shaped stringers, because they include opposing flanges and generally define a trapezoidal volume when viewed in cross-section. The flanges provide surfaces for operative coupling of the stringers to the skin of the composite fuselage. When operatively coupled to the skin, the flanges create steps, or joggles, at the terminuses of the flanges relative to the skin. These steps may add complexity or introduce less than desirable characteristics in the overall structure.